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I am new to relativity ,So please correct me If I am wrong. In the case I have mentioned, In a gravity free space, Let us assume a stationary observer and an observer moving with a velocity 'V' w.r.t to the stationary observer.

The stationary observer looks at an event taking place very far away('X') at time 't' So the moving observer's reference (the event is taking place far away for the moving observer as well) of space time can be calculated using Lorentz transformation. if 'V' is considerably small compared to speed of light, then the transformation for space will be similar to Galilean transformation, but since the distance of the event taking place is very large the time transformation will not be Galilean. ( because of the term (V*X)/C^2)

A light year being of the order 10^16 and all objects in universe being beyond this distance, does that mean an observer moving with a speed of 10 m/s will have relativistic effects in significant form recording an event like star explosion, wobbling effects, light variation etc?

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marked as duplicate by John Rennie, ACuriousMind, Community Jul 14 '16 at 13:20

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An observer moving through space relative to the matter in that space will certainly see space foreshorten in the direction of movement. If that observer is moving almost at light speed (relative to the matter in space) then that observer will see all space become almost as flat as a pancake. Specifically, the effect is that the angle of an object has changed from the forward direction. For example, an object that is directly forward will still appear directly forward, and an object that was at 45 degrees from directly forward (when the observer was stationary with it) will appear to have moved closer to the side of the observer (the angle from the forward direction will increase). However, this change of angle is unrelated to the distance. So the effect isn't related to distance of the object. (BTW, there are actually other effects that IMO don't apply to this question)

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